# Transitively normal subgroup of normal subgroup

From Groupprops

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: transitively normal subgroup and normal subgroup

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## Definition

### Definition with symbols

A subgroup of a group is termed a **transitively normal subgroup of normal subgroup** if there exists a subgroup of containing such that is a normal subgroup of and is a transitively normal subgroup of .